Abstract. It is well known that for the simpler problem of constructing translation
invariants of grey scale images (1D, 2D or 3D) central moments can be used. There
are plain closed formulae expressing them in terms of the ordinary geometrical moments.
Moreover, central moments are ordinary moments of the properly normalized image.
In this paper we present moment invariants for the more involved problem of rotations
and reflections of 3D density objects, having exactly the same qualities as those mentio­
ned above of central moments.
The mathematical analysis of this problem is complicated mainly due to noncommutati­